[R-meta] fixed-effect multivariate model interpretation

See for example the Gleser & Olkin chapter:

Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes.
In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of
research synthesis and meta-analysis (2nd ed., pp. 357?376). New York:
Russell Sage Foundation.

https://www.metafor-project.org/doku.php/analyses:gleser2009

Best,
Wolfgang

-----Original Message-----
From: Filippo Gambarota [mailto:filippo.gambarota at gmail.com]
Sent: Monday, 03 January, 2022 18:02
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] fixed-effect multivariate model interpretation

Ah great! do you have any references for this? because I would like to

clearly

understand what is going on. Cochrane's Q-statistic is the deviation of

each

study from the estimated average effect weighted by the precision. In

this case,

the "average" effect is the average between outcomes? Or the formula is
different?
Thank you!

On Mon, 3 Jan 2022 at 17:12, Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
It's just the multivariate version of Cochrane's Q-test. It does not

estimate a

random-effects model. It simply tests whether the observed amount of

variability

is larger than expected based on the sampling variances (and their

covariances

when V includes those) and any moderators specified.

Best,
Wolfgang

-----Original Message-----
From: Filippo Gambarota [mailto:filippo.gambarota at gmail.com]
Sent: Monday, 03 January, 2022 17:11
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] fixed-effect multivariate model interpretation

Thank you Wolfgang!
So my related question is how this residual heterogeneity is estimated

in order

to compute the Q statistic? Because if the model is still estimating and

testing

the presence of heterogeneity, from a multivariate model I would have

expected

one residual heterogeneity term for each outcome (the same as I have one

tau per

outcome if I fit the random-effect version).

On Mon, 3 Jan 2022 at 16:50, Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Hi Filippo,

You can *assume* that there is no residual heterogeneity, but there may

be. That

is what the test of residual heterogeneity is testing here (whether your
assumption is correct or not).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:

r-sig-meta-analysis-bounces at r-project.org] On

Behalf Of Filippo Gambarota
Sent: Monday, 03 January, 2022 16:42
To: R meta
Subject: [R-meta] fixed-effect multivariate model interpretation

Hello!
I'm fitting for the first time a multivariate fixed-effect model using
metafor. The code is:

```
rma.mv(yi, V, mods = ~ 0 + outcome, data = data, test = "t")
```
Where V is the block variance-covariance matrix created with vcalc()
that represents the covariance between different outcome levels within
each study. The outcome is a factor that represents different effect
sizes measured on the same participants within a study.
The model as expected did not estimate tau for each outcome and test
all coefficients (each outcome mean with this parametrization) against
0 (both the omnibus test and each beta). My question is about the
*residual heterogeneity* parameter and the associated Q test. Under
this model, I should have assumed that there is no heterogeneity
within each outcome level so I'm not sure how to interpret the
residual heterogeneity in this case.
Thank you!
Filippo

--
Filippo Gambarota
PhD Student - University of Padova
Department of Developmental and Social Psychology
Website: filippogambarota.netlify.app
Research Group: Colab   Psicostat